Sparta and PSV Eindhoven At Sparta, Van Beveren trained with coach
Wiel Coerver, who turned out to be instrumental in his development. They would frequently hold training sessions together three times a day. Van Beveren reached the fifth place twice with Sparta and in his last season, that spot enabled them to enter the
Inter-Cities Fairs Cup. In 1970, the ambitious Van Beveren aimed for a bigger club, and
Ajax,
Feyenoord,
Real Madrid and
PSV Eindhoven tried to sign him. Real Madrid had to cancel the deal because the
Spanish league was being closed for foreigners. Of the remaining clubs, only PSV managed to meet the financial demands from Sparta and Van Beveren, with the transfer fee being 1 million
Guilder. In his first season, the team reached the semi-finals of the
European Cup Winners' Cup, but were eliminated by Real Madrid. In the following years, Van Beveren established himself as PSV's first goalkeeper choice; in 1973 he signed a new seven-year contract with the club. Van Beveren had an unlucky start to the
1977–78 season when he collided with the woodwork in an exhibition match against Hapert, leaving him with a concussion. In the
UEFA Cup final, Van Beveren kept a clean sheet in both matches. PSV won 3–0 on aggregate and Van Beveren lifted his first and only European trophy. An incident in 1978 motivated Van Beveren to leave the Netherlands. Throughout his international career, a public dispute between Van Beveren and
Johan Cruyff resulted in the public siding with the latter and viewing Van Beveren's international retirement as a 'betrayal'. When he was asked to appear as a pundit for a
1978 FIFA World Cup national team match, the Dutch public broadcast channel received many threats aimed at Van Beveren, his property and his family. His television appearance was cancelled, and that night Van Beveren decided to leave the Netherlands for good. He remained at the club for three years, at the time competing in the
North American Soccer League (NASL). Because of the demise of the NASL after the 1983 season, Van Beveren was left without a club. In April 1984, he went on to play in the
Major Indoor Soccer League (MISL) by joining the
Dallas Sidekicks. Van Beveren was the first player ever to be signed by the newly founded Sidekicks. His first season was disappointing: he lost 22 of the 30 matches he appeared in, and the Sidekicks ended last in the league. In the
1985–86 season, he played three more games for the club, before being officially released in February 1986. == International career ==